Question

How many terms are there in an A.P. whose first and fifth terms are – 14 and 2, respectively and the last term is 62?

Answer 1

a = –14, a₅ = 2, a_n= 62

a₅ = a + (5 – 1)d   ...[∵ a_n = a + (n – 1)d]

`\implies` 2 = –14 + 4d

`\implies` 4d = 16

`\implies` d = 4

Now, a_n = 62

`\implies` a + (n – 1)d = 62

`\implies` –14 + (n – 1)4 = 62   ...(∵ a = –14, d = 4)

`\implies` (n – 1)4 = 76

`\implies` n – 1 = `76/4` = 19

`\implies` n = 19 + 1 = 20

∴ There are 20 terms in an A.P.